/* crypto/ec/ec2_smpl.c */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. * * The Elliptic Curve Public-Key Crypto Library (ECC Code) included * herein is developed by SUN MICROSYSTEMS, INC., and is contributed * to the OpenSSL project. * * The ECC Code is licensed pursuant to the OpenSSL open source * license provided below. * * The software is originally written by Sheueling Chang Shantz and * Douglas Stebila of Sun Microsystems Laboratories. * */ /* ==================================================================== * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ #include #include "ec_lcl.h" const EC_METHOD *EC_GF2m_simple_method(void) { static const EC_METHOD ret = { NID_X9_62_characteristic_two_field, ec_GF2m_simple_group_init, ec_GF2m_simple_group_finish, ec_GF2m_simple_group_clear_finish, ec_GF2m_simple_group_copy, ec_GF2m_simple_group_set_curve, ec_GF2m_simple_group_get_curve, ec_GF2m_simple_group_get_degree, ec_GF2m_simple_group_check_discriminant, ec_GF2m_simple_point_init, ec_GF2m_simple_point_finish, ec_GF2m_simple_point_clear_finish, ec_GF2m_simple_point_copy, ec_GF2m_simple_point_set_to_infinity, 0 /* set_Jprojective_coordinates_GFp */, 0 /* get_Jprojective_coordinates_GFp */, ec_GF2m_simple_point_set_affine_coordinates, ec_GF2m_simple_point_get_affine_coordinates, ec_GF2m_simple_set_compressed_coordinates, ec_GF2m_simple_point2oct, ec_GF2m_simple_oct2point, ec_GF2m_simple_add, ec_GF2m_simple_dbl, ec_GF2m_simple_invert, ec_GF2m_simple_is_at_infinity, ec_GF2m_simple_is_on_curve, ec_GF2m_simple_cmp, ec_GF2m_simple_make_affine, ec_GF2m_simple_points_make_affine, /* the following three method functions are defined in ec2_mult.c */ ec_GF2m_simple_mul, ec_GF2m_precompute_mult, ec_GF2m_have_precompute_mult, ec_GF2m_simple_field_mul, ec_GF2m_simple_field_sqr, ec_GF2m_simple_field_div, 0 /* field_encode */, 0 /* field_decode */, 0 /* field_set_to_one */ }; return &ret; } /* Initialize a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_new. */ int ec_GF2m_simple_group_init(EC_GROUP *group) { BN_init(&group->field); BN_init(&group->a); BN_init(&group->b); return 1; } /* Free a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_free. */ void ec_GF2m_simple_group_finish(EC_GROUP *group) { BN_free(&group->field); BN_free(&group->a); BN_free(&group->b); } /* Clear and free a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_clear_free. */ void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) { BN_clear_free(&group->field); BN_clear_free(&group->a); BN_clear_free(&group->b); group->poly[0] = 0; group->poly[1] = 0; group->poly[2] = 0; group->poly[3] = 0; group->poly[4] = 0; } /* Copy a GF(2^m)-based EC_GROUP structure. * Note that all other members are handled by EC_GROUP_copy. */ int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) { int i; if (!BN_copy(&dest->field, &src->field)) return 0; if (!BN_copy(&dest->a, &src->a)) return 0; if (!BN_copy(&dest->b, &src->b)) return 0; dest->poly[0] = src->poly[0]; dest->poly[1] = src->poly[1]; dest->poly[2] = src->poly[2]; dest->poly[3] = src->poly[3]; dest->poly[4] = src->poly[4]; bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2); bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2); for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0; for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0; return 1; } /* Set the curve parameters of an EC_GROUP structure. */ int ec_GF2m_simple_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { int ret = 0, i; /* group->field */ if (!BN_copy(&group->field, p)) goto err; i = BN_GF2m_poly2arr(&group->field, group->poly, 5); if ((i != 5) && (i != 3)) { ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); goto err; } /* group->a */ if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err; bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2); for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0; /* group->b */ if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err; bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2); for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0; ret = 1; err: return ret; } /* Get the curve parameters of an EC_GROUP structure. * If p, a, or b are NULL then there values will not be set but the method will return with success. */ int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) { int ret = 0; if (p != NULL) { if (!BN_copy(p, &group->field)) return 0; } if (a != NULL) { if (!BN_copy(a, &group->a)) goto err; } if (b != NULL) { if (!BN_copy(b, &group->b)) goto err; } ret = 1; err: return ret; } /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */ int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) { return BN_num_bits(&group->field)-1; } /* Checks the discriminant of the curve. * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) */ int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) { int ret = 0; BIGNUM *b; BN_CTX *new_ctx = NULL; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) { ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); goto err; } } BN_CTX_start(ctx); b = BN_CTX_get(ctx); if (b == NULL) goto err; if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err; /* check the discriminant: * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) */ if (BN_is_zero(b)) goto err; ret = 1; err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; } /* Initializes an EC_POINT. */ int ec_GF2m_simple_point_init(EC_POINT *point) { BN_init(&point->X); BN_init(&point->Y); BN_init(&point->Z); return 1; } /* Frees an EC_POINT. */ void ec_GF2m_simple_point_finish(EC_POINT *point) { BN_free(&point->X); BN_free(&point->Y); BN_free(&point->Z); } /* Clears and frees an EC_POINT. */ void ec_GF2m_simple_point_clear_finish(EC_POINT *point) { BN_clear_free(&point->X); BN_clear_free(&point->Y); BN_clear_free(&point->Z); point->Z_is_one = 0; } /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */ int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) { if (!BN_copy(&dest->X, &src->X)) return 0; if (!BN_copy(&dest->Y, &src->Y)) return 0; if (!BN_copy(&dest->Z, &src->Z)) return 0; dest->Z_is_one = src->Z_is_one; return 1; } /* Set an EC_POINT to the point at infinity. * A point at infinity is represented by having Z=0. */ int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) { point->Z_is_one = 0; BN_zero(&point->Z); return 1; } /* Set the coordinates of an EC_POINT using affine coordinates. * Note that the simple implementation only uses affine coordinates. */ int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) { int ret = 0; if (x == NULL || y == NULL) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); return 0; } if (!BN_copy(&point->X, x)) goto err; BN_set_negative(&point->X, 0); if (!BN_copy(&point->Y, y)) goto err; BN_set_negative(&point->Y, 0); if (!BN_copy(&point->Z, BN_value_one())) goto err; BN_set_negative(&point->Z, 0); point->Z_is_one = 1; ret = 1; err: return ret; } /* Gets the affine coordinates of an EC_POINT. * Note that the simple implementation only uses affine coordinates. */ int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) { int ret = 0; if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); return 0; } if (BN_cmp(&point->Z, BN_value_one())) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } if (x != NULL) { if (!BN_copy(x, &point->X)) goto err; BN_set_negative(x, 0); } if (y != NULL) { if (!BN_copy(y, &point->Y)) goto err; BN_set_negative(y, 0); } ret = 1; err: return ret; } /* Calculates and sets the affine coordinates of an EC_POINT from the given * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. * Note that the simple implementation only uses affine coordinates. * * The method is from the following publication: * * Harper, Menezes, Vanstone: * "Public-Key Cryptosystems with Very Small Key Lengths", * EUROCRYPT '92, Springer-Verlag LNCS 658, * published February 1993 * * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe * the same method, but claim no priority date earlier than July 29, 1994 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art). */ int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, const BIGNUM *x_, int y_bit, BN_CTX *ctx) { BN_CTX *new_ctx = NULL; BIGNUM *tmp, *x, *y, *z; int ret = 0, z0; /* clear error queue */ ERR_clear_error(); if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } y_bit = (y_bit != 0) ? 1 : 0; BN_CTX_start(ctx); tmp = BN_CTX_get(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); z = BN_CTX_get(ctx); if (z == NULL) goto err; if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err; if (BN_is_zero(x)) { if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err; } else { if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err; if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err; if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err; if (!BN_GF2m_add(tmp, x, tmp)) goto err; if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) { unsigned long err = ERR_peek_last_error(); if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) { ERR_clear_error(); ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); } else ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); goto err; } z0 = (BN_is_odd(z)) ? 1 : 0; if (!group->meth->field_mul(group, y, x, z, ctx)) goto err; if (z0 != y_bit) { if (!BN_GF2m_add(y, y, x)) goto err; } } if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; ret = 1; err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; } /* Converts an EC_POINT to an octet string. * If buf is NULL, the encoded length will be returned. * If the length len of buf is smaller than required an error will be returned. */ size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, unsigned char *buf, size_t len, BN_CTX *ctx) { size_t ret; BN_CTX *new_ctx = NULL; int used_ctx = 0; BIGNUM *x, *y, *yxi; size_t field_len, i, skip; if ((form != POINT_CONVERSION_COMPRESSED) && (form != POINT_CONVERSION_UNCOMPRESSED) && (form != POINT_CONVERSION_HYBRID)) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); goto err; } if (EC_POINT_is_at_infinity(group, point)) { /* encodes to a single 0 octet */ if (buf != NULL) { if (len < 1) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); return 0; } buf[0] = 0; } return 1; } /* ret := required output buffer length */ field_len = (EC_GROUP_get_degree(group) + 7) / 8; ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; /* if 'buf' is NULL, just return required length */ if (buf != NULL) { if (len < ret) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); goto err; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); used_ctx = 1; x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); yxi = BN_CTX_get(ctx); if (yxi == NULL) goto err; if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; buf[0] = form; if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) { if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; if (BN_is_odd(yxi)) buf[0]++; } i = 1; skip = field_len - BN_num_bytes(x); if (skip > field_len) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; } while (skip > 0) { buf[i++] = 0; skip--; } skip = BN_bn2bin(x, buf + i); i += skip; if (i != 1 + field_len) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; } if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) { skip = field_len - BN_num_bytes(y); if (skip > field_len) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; } while (skip > 0) { buf[i++] = 0; skip--; } skip = BN_bn2bin(y, buf + i); i += skip; } if (i != ret) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); goto err; } } if (used_ctx) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; err: if (used_ctx) BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return 0; } /* Converts an octet string representation to an EC_POINT. * Note that the simple implementation only uses affine coordinates. */ int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, const unsigned char *buf, size_t len, BN_CTX *ctx) { point_conversion_form_t form; int y_bit; BN_CTX *new_ctx = NULL; BIGNUM *x, *y, *yxi; size_t field_len, enc_len; int ret = 0; if (len == 0) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); return 0; } form = buf[0]; y_bit = form & 1; form = form & ~1U; if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) && (form != POINT_CONVERSION_UNCOMPRESSED) && (form != POINT_CONVERSION_HYBRID)) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; } if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; } if (form == 0) { if (len != 1) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; } return EC_POINT_set_to_infinity(group, point); } field_len = (EC_GROUP_get_degree(group) + 7) / 8; enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; if (len != enc_len) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); return 0; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); yxi = BN_CTX_get(ctx); if (yxi == NULL) goto err; if (!BN_bin2bn(buf + 1, field_len, x)) goto err; if (BN_ucmp(x, &group->field) >= 0) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; } if (form == POINT_CONVERSION_COMPRESSED) { if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err; } else { if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; if (BN_ucmp(y, &group->field) >= 0) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; } if (form == POINT_CONVERSION_HYBRID) { if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; if (y_bit != BN_is_odd(yxi)) { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); goto err; } } if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; } if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ { ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); goto err; } ret = 1; err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; } /* Computes a + b and stores the result in r. r could be a or b, a could be b. * Uses algorithm A.10.2 of IEEE P1363. */ int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { BN_CTX *new_ctx = NULL; BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; int ret = 0; if (EC_POINT_is_at_infinity(group, a)) { if (!EC_POINT_copy(r, b)) return 0; return 1; } if (EC_POINT_is_at_infinity(group, b)) { if (!EC_POINT_copy(r, a)) return 0; return 1; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); x0 = BN_CTX_get(ctx); y0 = BN_CTX_get(ctx); x1 = BN_CTX_get(ctx); y1 = BN_CTX_get(ctx); x2 = BN_CTX_get(ctx); y2 = BN_CTX_get(ctx); s = BN_CTX_get(ctx); t = BN_CTX_get(ctx); if (t == NULL) goto err; if (a->Z_is_one) { if (!BN_copy(x0, &a->X)) goto err; if (!BN_copy(y0, &a->Y)) goto err; } else { if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err; } if (b->Z_is_one) { if (!BN_copy(x1, &b->X)) goto err; if (!BN_copy(y1, &b->Y)) goto err; } else { if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err; } if (BN_GF2m_cmp(x0, x1)) { if (!BN_GF2m_add(t, x0, x1)) goto err; if (!BN_GF2m_add(s, y0, y1)) goto err; if (!group->meth->field_div(group, s, s, t, ctx)) goto err; if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; if (!BN_GF2m_add(x2, x2, &group->a)) goto err; if (!BN_GF2m_add(x2, x2, s)) goto err; if (!BN_GF2m_add(x2, x2, t)) goto err; } else { if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { if (!EC_POINT_set_to_infinity(group, r)) goto err; ret = 1; goto err; } if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err; if (!BN_GF2m_add(s, s, x1)) goto err; if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; if (!BN_GF2m_add(x2, x2, s)) goto err; if (!BN_GF2m_add(x2, x2, &group->a)) goto err; } if (!BN_GF2m_add(y2, x1, x2)) goto err; if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err; if (!BN_GF2m_add(y2, y2, x2)) goto err; if (!BN_GF2m_add(y2, y2, y1)) goto err; if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err; ret = 1; err: BN_CTX_end(ctx); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; } /* Computes 2 * a and stores the result in r. r could be a. * Uses algorithm A.10.2 of IEEE P1363. */ int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) { return ec_GF2m_simple_add(group, r, a, a, ctx); } int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) { if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) /* point is its own inverse */ return 1; if (!EC_POINT_make_affine(group, point, ctx)) return 0; return BN_GF2m_add(&point->Y, &point->X, &point->Y); } /* Indicates whether the given point is the point at infinity. */ int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) { return BN_is_zero(&point->Z); } /* Determines whether the given EC_POINT is an actual point on the curve defined * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: * y^2 + x*y = x^3 + a*x^2 + b. */ int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) { int ret = -1; BN_CTX *new_ctx = NULL; BIGNUM *lh, *y2; int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); if (EC_POINT_is_at_infinity(group, point)) return 1; field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; /* only support affine coordinates */ if (!point->Z_is_one) goto err; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; } BN_CTX_start(ctx); y2 = BN_CTX_get(ctx); lh = BN_CTX_get(ctx); if (lh == NULL) goto err; /* We have a curve defined by a Weierstrass equation * y^2 + x*y = x^3 + a*x^2 + b. * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 * <=> ((x + a) * x + y ) * x + b + y^2 = 0 */ if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err; if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; if (!BN_GF2m_add(lh, lh, &point->Y)) goto err; if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; if (!BN_GF2m_add(lh, lh, &group->b)) goto err; if (!field_sqr(group, y2, &point->Y, ctx)) goto err; if (!BN_GF2m_add(lh, lh, y2)) goto err; ret = BN_is_zero(lh); err: if (ctx) BN_CTX_end(ctx); if (new_ctx) BN_CTX_free(new_ctx); return ret; } /* Indicates whether two points are equal. * Return values: * -1 error * 0 equal (in affine coordinates) * 1 not equal */ int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { BIGNUM *aX, *aY, *bX, *bY; BN_CTX *new_ctx = NULL; int ret = -1; if (EC_POINT_is_at_infinity(group, a)) { return EC_POINT_is_at_infinity(group, b) ? 0 : 1; } if (a->Z_is_one && b->Z_is_one) { return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; } BN_CTX_start(ctx); aX = BN_CTX_get(ctx); aY = BN_CTX_get(ctx); bX = BN_CTX_get(ctx); bY = BN_CTX_get(ctx); if (bY == NULL) goto err; if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err; if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err; ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; err: if (ctx) BN_CTX_end(ctx); if (new_ctx) BN_CTX_free(new_ctx); return ret; } /* Forces the given EC_POINT to internally use affine coordinates. */ int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) { BN_CTX *new_ctx = NULL; BIGNUM *x, *y; int ret = 0; if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) return 1; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); if (y == NULL) goto err; if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; if (!BN_copy(&point->X, x)) goto err; if (!BN_copy(&point->Y, y)) goto err; if (!BN_one(&point->Z)) goto err; ret = 1; err: if (ctx) BN_CTX_end(ctx); if (new_ctx) BN_CTX_free(new_ctx); return ret; } /* Forces each of the EC_POINTs in the given array to use affine coordinates. */ int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) { size_t i; for (i = 0; i < num; i++) { if (!group->meth->make_affine(group, points[i], ctx)) return 0; } return 1; } /* Wrapper to simple binary polynomial field multiplication implementation. */ int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); } /* Wrapper to simple binary polynomial field squaring implementation. */ int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) { return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); } /* Wrapper to simple binary polynomial field division implementation. */ int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { return BN_GF2m_mod_div(r, a, b, &group->field, ctx); }